find the solution set of x ^log base 5 of x >5
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Answer:
log
5
(
x
)
+
log
5
(
x
+
1
)
=
log
5
(
20
)
Simplify the left side.
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log
5
(
x
2
+
x
)
=
log
5
(
20
)
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
x
2
+
x
=
20
Solve for
x
.
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x
=
4
,
−
5
Exclude the solutions that do not make
log
5
(
x
)
+
log
5
(
x
+
1
)
=
log
5
(
20
)
true.
x
=
4
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